Sunday, July 6, 2014

Dragon Boat Physics 101: Levers

I have always been strongly against choking up on the paddle. Your bottom hand should be just above the blade and it should stay there. I've been picking on this particular element heavy in the past month and have been asked why a couple times. The reasoning for choking up is usually to get deeper in the water (something that can be corrected by dropping your body more), but this comes at a cost of leverage on the paddle. You will notice that the further up your bottom hand climbs, the less control you have over the paddle and it becomes harder to pull the water. That's the leverage that you're losing.
But that had me thinking: leverage (by physics definition) is the presence of mechanical advantage through a lever. So parts of the dragon boat stroke must follow that of the lever. So let's explore this idea by modelling the stroke as a simple mechanical system and figure out what we can learn from it.The Lever

Simple lever at equilibrium

A lever is a movable bar that pivots over a fulcrum at a fixed point. The law of the lever states that the force applied to the lever is proportional to the distance from the point of force application and the fulcrum. So at equilibrium, F1*L1 = F2*L2

Lever with offset fulcrum

When L1 and L2 are not equal, then to stay at equilibrium, the force F1 must be proportionally greater than F2.

Single sided lever

This is also true when the fulcrum is a fixed point on the end of the lever. To be in equilibrium, the upward force at L1 must be proportionally greater than the downward force of F2 at L2.

The takeaway here is that for maximum mechanical advantage, you want to apply force into a system where the length from your force application to the fulcrum is as great as possible.

Modelling The Stroke

To attempt to apply this information to the stroke, we need to figure out how the stroke is similar to a lever. Since we affect the paddle is two places (the top hand and the bottom hand), we can assume one is the force and the other is the fulcrum.

Top-hand Fulcrum Model

Top-hand fulcrum model

The first model I will consider is that the top hand is a fixed point and the bottom hand is responsible for pulling on the paddle to apply force onto the blade. This is a fair assumption and I've seen people paddle this way: top hand is held up (straight arms and all) and the bottom hand is pulling. The first test is to figure out whether what we know about bottom hand position is true for leverage in this model. As the bottom arm rises, you actually need to apply more force on the blade tip because the distance from your point of force application to the fulcrum is decreasing while the distance from the fulcrum to the output force (the blade) is constant.

The top-hand model as a lever

In our original lever model, this would equivalent to having a load (a box in this case) at the bottom of a lever with the fulcrum attached to the opposite end. To lift the box, we grab the lever just above the box and lift. This sounds like a silly way to do this, because it would actually be easier (in terms of amount of work) to just lift the box directly instead of using a lever, but that's the disadvantage to this model: it is inherently inefficient.

So what we learn from this model is that chocking up on the paddle is actually decreasing our force output into the water. Now the problem here is that according to this model we always have loses of force output due to the difference of the distance between the bottom hand and the blade.

Bottom-hand Fulcrum Model

Bottom-hand fulcrum model

So let's look at the next model: where the bottom hand is the fulcrum and the top hand is responsible for applying force. Let's put it through the leverage test: what happens when the bottom hand moves up? As the bottom hand rises the fulcrum changes, and the distance from the top hand to fulcrum decreases as the distance from the blade to fulcrum increases. This is consistent with making it more difficult to paddle as your bottom hand rises.

The bottom-hand model as a lever

If we once again restructure the problem as our simple lever, it will be like having a box at the bottom of a lever with the fulcrum placed in the middle. When you jump onto the opposite end (i.e. applying an opposite force), the box will rise. As the fulcrum is moved closer to the box, it will become easier to lift it. If we relate it back to the dragon boat paddle, that means that the force applied on the water is proportional to the distance from the top hand to the bottom hand (fulcrum) to the blade. So the lower the bottom hand is place, the more efficient. Additionally, this implies that going with a longer paddle will actually increase your force output on the blade in relation to the force you put on the top hand (with caveats).

But this model has problems. The most obvious is that the bottom hand does not stay stationary when paddling because you would end up with a very short stroke. But that doesn't invalidate this model all together.

Applying a forward translation to the bottom-hand fulcrum model

Well we know that as you take your stroke, you actually mode forward (due to the boat moving forward). So I took the bottom-hand fulcrum model and shifted each frame forward. From an outside perspective it looks now like the pivot is the bottom of the blade. From the paddler's perspective, it feels like they are applying force to the top arm as the bottom hand sweeps backwards. Additionally this sweeping of the bottom arm will actually add overall force the the system. But for the lever properties to hold, the bottom arm must be held firm and ideally straight. Drawing the fulcrum back with a bent elbow actually lowers the amount of force that can be applied to it making it no longer act as a fixed point.

Conclusion

Assuming the stroke can be modeled as a lever mechanical system, we can learn that maximum force application efficiency can be achieved through applying force on the top hand. The bottom hand will still be involved to move backwards as the boat moves forward, but to act as a fulcrum, the bottom arm should be firm and solid (i.e. straight elbow).

Also, in all possible cases, choking up on the paddle will decrease force output into the water.